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We can work out the growth rates for 1, 2 and 5 years at 7.1% per annum compounded quarterly.

The quarterly rate is 7.1/4=1.775%.

Growth rates:

1 yr: 1.01775⁴=1.0729 approx

2 yr: 1.01775⁸=1.1511 approx

5 yr: 1.01775²⁰=1.4217 approx

We can apply the growth rates to any of the amounts.

To pay off \$4075 in 2 years’ time would have needed an investment of 4075/1.1511=\$3539.96 now. In a year’s time this would grow to 3539.96(1.0729)=\$3798.07.

To pay off \$6725 in 5 years’ time would have needed an investment of 6725/1.4217=\$4730.10 now. In a year’s time this would grow to 4730.10(1.0729)=\$5074.98.

Therefore the total amount to be paid in a year’s time is 3798.07+5074.98=\$8873.05.

This calculation takes into account the fact that the debts are paid early so the amounts to be paid are correspondingly reduced from \$10800.

The graph illustrates the calculation.

by Top Rated User (627k points)

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